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Networks are known to be prone to node or link failures. A central issue in the analysis of complex networks is the assessment of their robustness and vulnerability. A network is usually represented by an undirected simple graph where vertices represent processors and edges represent links between processors. Different approaches to properly define a measure for graph vulnerability has been proposed so far. The distance d(i,j) between any two vertices i and j in a graph is the number of edges in a shortest path between i and j. If there is no path connecting i and j, then d(i,j) = ? . Latora and Marchiori introduced the measure of efficiency between vertices in a graph in 2001. The unweighted efficiency between two vertices i and j is defined to be ?ij=1/dij for all i ? j. The global efficiency of a graph (Formula presented.) which is simply the average of the efficiencies over all pairs of distinct n vertices. In this paper, we study the global efficiency of special graphs. The behavior of this distance-related parameter on special graphs is taken into account by graphical analysis. © 2015 Academic Publications, Ltd. |
